Издательство InTech, 2011, -268 pp.Discrete wavelet transform (DWT) algorithms have become standards tools for processing of signals and images in several areas in research and industry. The first DWT structures were based on the compactly supported conjugate quadrature filters (CQFs). However, a drawback in CQFs is related to the nonlinear phase effects such as image blurring and spatial dislocations in multi-scale analyses. On the contrary, in biorthogonal discrete wavelet transform (BDWT) the scaling and wavelet filters are symmetric and linear phase. The BDWT algorithms are commonly constructed by a ladder-type network called lifting scheme. The procedure consists of sequential down and uplifting steps and the reconstruction of the signal is made by running the lifting network in reverse order. Efficient lifting BDWT structures have been developed for VLSI and microprocessor applications. The analysis and synthesis filters can be implemented by integer arithmetic using only register shift s and summations. Many BDWT-based data and image processing tools have outperformed the conventional discrete cosine transform (DCT) -based approaches. For example, in JPEG2000 Standard the DCT has been replaced by the lifting BDWT.
As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. One of the main difficulties in multi-scale analysis is the dependency of the total energy of the wavelet coefficients in different scales on the fractional shift s of the analysed signal. If we have a discrete signal x[n] and the corresponding time shift ed signal x[n-τ], where τ ∈ [0,1], there may exist a significant difference in the energy of the wavelet coefficients as a function of the time shift . In shift invariant methods the real and imaginary parts of the complex wavelet coefficients are approximately a Hilbert transform pair. The energy of the wavelet coefficients equals the envelope, which provides smoothness and approximate shift -invariance. Using two parallel DWT banks, which are constructed so that the impulse responses of the scaling filters have half-sample delayed versions of each other, the corresponding wavelets are a Hilbert transform pair. The dual-tree CQF wavelet filters do not have coefficient symmetry and the nonlinearity interferes with the spatial timing in different scales and prevents accurate statistical correlations. Therefore the current developments in theory and applications of wavelets are concentrated on the dual-tree BDWT structures.
This book reviews the recent progress in theory and applications of wavelet transform algorithms. The book is intended to cover a wide range of methods (e.g. lifting DWT, shift invariance, 2D image enhancement) for constructing DWTs and to illustrate the utilization of DWTs in several non-stationary problems and in biomedical as well as industrial applications. It is organized into four major parts. Part I focuses on non-time series, non-stationary vibration and sound signals in the vehicle engineering and motor fault detection. Part II addresses image processing and analysis applications such as image denoising and contrast enhancement, and face recognition. Part III is devoted to biomedical applications, including ECG signal compression, multi-scale analysis of EEG signals and classification of medical images in computer aided diagnosis. Finally, Part IV describes how DWT can be utilized in wireless digital communication systems and synchronization of power converters.
It should be pointed that the book comprises of both tutorial and advanced material. Therefore, it is intended to be a reference text for graduate students and researchers to obtain in-depth knowledge on specific applications. The editor is indebted to all co-authors for giving their valuable time and expertise in constructing this book. The technical editors are also acknowledged for their tedious support and help.
